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When a binomial is squared, the resulting expression is a perfect square trinomial.
(a + b)^2=a^2 + 2ab+b^2 (a - b)^2=a^2 - 2ab+b^2
For simplicity, depending on the sign of the binomial, these two identities can be expressed as one.
(a ± b)^2=a^2 ± 2ab+b^2
This identity can be shown by first rewriting the square as a product.
a^2=a* a
Distribute (a+b)
Distribute a
Distribute b
Commutative Property of Multiplication
Add terms
It has been shown that (a+b)^2=a^2+2ab+b^2.
In this case, when one term of the binomial is subtracted from the other, the middle term of the perfect square trinomial will instead be negative.
a^2=a* a
Distribute (a-b)
Distribute a
Distribute - b
Commutative Property of Multiplication
Subtract terms
It has been shown that (a-b)^2=a^2-2ab+b^2.